Difference between revisions of "Team:UESTC-China/Model2"

 
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<div class="firstless" >
 
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   <ul class="f_mh mya"  style="display:none;margin-left:5px">
 
   <ul class="f_mh mya"  style="display:none;margin-left:5px">
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<li  class="active"><a href="#title_1">Basic Part</a></li>
+
<li  class="active"><a href="#title_1">Overview</a></li>
 
<li ><a href="#title_2">Goals</a></li>
 
<li ><a href="#title_2">Goals</a></li>
 
<li ><a href="#title_3">Factor screening</a></li>
 
<li ><a href="#title_3">Factor screening</a></li>
 
<li ><a href="#title_4">Experiment design</a></li>
 
<li ><a href="#title_4">Experiment design</a></li>
−
<li ><a href="#title_5">Optimal solution</a></li>
+
                <li ><a href="#title_5">Optimal solution</a></li>
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<li ><a href="#title_6">References</a></li>
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                <li ><a href="#title_6">References</a></li>
 
   </ul>
 
   </ul>
 
   <a href="#"> <img  class="up" src="https://static.igem.org/mediawiki/2019/7/7d/T--UESTC-China--up.png" alt="logo" width="100%"> </a> </div>
 
   <a href="#"> <img  class="up" src="https://static.igem.org/mediawiki/2019/7/7d/T--UESTC-China--up.png" alt="logo" width="100%"> </a> </div>
  
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<div class="container col-5">
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<div class="part">
 
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<p>Overview</p>
 
<p>Overview</p>
 
</div>
 
</div>
 +
 
<div class="mainbody">
 
<div class="mainbody">
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Due to minor difference between the data of the experimental group and the control group in the experiments, we performed a significance test to verify the function of CrpP. Then considering the low degradation rate, we are going to optimize the external degradation conditions of the engineered bacteria.</div>
+
In order to find the optimal degradation conditions for engineered <i>E.coli</i>, we found the main factors affecting the degradation rate from the related paper[1]. Firstly, we used the Plackett-Burman design to screen factors. In the future we can get the important factors by experimental data. Secondly, the Box-Behnken design was used in the experimental design to reflect objective reality with fewer experiments. According to the experimental results, the response surface equation can be obtained, and optimal degradation conditions can be found. Finally, after obtaining the extreme value of the equation (optimal degradation conditions), it can be verified by experiments in the future.</div>
−
<div class="mainbody">
+
−
In order to find the optimal degradation conditions for engineered E. coli, we found the main factors affecting the degradation rate from the paper. Firstly, we used the Plackett-Burman design to screen factors. In the future we can get the important factors by experimental data. Secondly, the Box-Behnken design was used in the experimental design to reflect objective reality with fewer experiments. According to the experimental results, the response surface equation can be obtained. Finally, after obtaining the extreme value of the equation (optimal degradation conditions), it can be verified by experiments.</div>
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</div>
 
</div>
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<div class="mainbody">
 
<div class="mainbody">
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1. verify the function of CrpP<br>
+
1. Screen all factors to obtain important factors affecting the degradation rate of CrpP enzyme<br>
−
2. Screen all factors to obtain important factors affecting the degradation rate of CrpP enzyme<br>
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2. Find the optimal working conditions for engineered <i>E.coli</i><br>
−
3. Find the optimal working conditions for engineered <i>E.coli</i><br>
+
3. To achieve the optimal CIP degradation rate with as little experimental cost as possible.
−
4. Try to save experimental cost and get optimal conditions with fewer experiments
+
 
</div>
 
</div>
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</div>
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</div>  
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<div class="part">
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<div class="bigtitle" id="title_2">
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<p>Verification of CrpP function</p>
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−
</div>
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−
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−
<div class="mainbody">
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−
Kolmogorov–Smirnov test <br>
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−
Firstly, we used the K-S test combined with SPSS software to test the normality of the data. The P values of the experimental group and the control group are greater than 0.05, so we can think that the experimental data of both groups are in accordance with normal distribution. The results are as follows:
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−
</div>
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−
<div class="mainbody table-responsive" style="border: 0;">
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−
<table class="table  table-hover mythree" >
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−
<caption>Table 1 One-Sample Kolmogorov-Smirnov Test</caption>
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−
<tbody>
+
−
<tr>
+
−
<th>VAR00001</th>
+
−
<th></th>
+
−
<th></th>
+
−
<th>VAR00002</th>
+
−
</tr>
+
−
<tr>
+
−
<th>1.00</th>
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−
<th>N</th>
+
−
<th></th>
+
−
<th>30</th>
+
−
</tr>
+
−
<tr>
+
−
<th></th>
+
−
<th>Normal Parameters</th>
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−
<th>Mean</th>
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−
<th>402223.7667
+
−
</th>
+
−
</tr>
+
−
<tr>
+
−
<th></th>
+
−
<th></th>
+
−
<th>Std. Deviation
+
−
</th>
+
−
<th>3219.62263
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−
</th>
+
−
</tr>
+
−
<tr>
+
−
<th></th>
+
−
<th>Most Extreme Differences
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−
</th>
+
−
<th>Absolut
+
−
</th>
+
−
<th>0.145
+
−
</th>
+
−
</tr>
+
−
<tr>
+
−
<th></th>
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−
<th></th>
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−
<th>Positive
+
−
</th>
+
−
<th>0.145
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−
</th>
+
−
</tr>
+
−
<tr>
+
−
<th></th>
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−
<th></th>
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−
<th>Negative
+
−
</th>
+
−
<th>-0.078
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−
</th>
+
−
</tr>
+
−
<tr>
+
−
<th></th>
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−
<th>Kolmogorov-Smirnov Z
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−
</th>
+
−
<th></th>
+
−
<th>0.796
+
−
</th>
+
−
</tr>
+
−
<tr>
+
−
<th></th>
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−
<th>Asymp. Sig. (2-tailed)
+
−
</th>
+
−
<th></th>
+
−
<th>0.55
+
−
</th>
+
−
</tr>
+
−
<tr>
+
−
<th>2.00</th>
+
−
<th>N</th>
+
−
<th></th>
+
−
<th>6</th>
+
−
</tr>
+
−
+
−
<tr>
+
−
<th></th>
+
−
<th>Normal Parameters
+
−
</th>
+
−
<th>Mean
+
−
</th>
+
−
<th>405566.6667
+
−
</th>
+
−
</tr>
+
−
+
−
<tr>
+
−
<th></th>
+
−
<th></th>
+
−
<th>Std. Deviation
+
−
</th>
+
−
<th>4449.85585
+
−
</th>
+
−
</tr>
+
−
<tr>
+
−
<th></th>
+
−
<th>Most Extreme Differences
+
−
</th>
+
−
<th>Absolut
+
−
</th>
+
−
<th>0.178
+
−
</th>
+
−
</tr>
+
−
<tr>
+
−
<th></th>
+
−
<th></th>
+
−
<th>Positive
+
−
</th>
+
−
<th>0.178
+
−
</th>
+
−
</tr>
+
−
<tr>
+
−
<th></th>
+
−
<th></th>
+
−
<th>Negative
+
−
</th>
+
−
<th>-0.157
+
−
</th>
+
−
</tr>
+
−
<tr>
+
−
<th></th>
+
−
<th>Kolmogorov-Smirnov Z
+
−
</th>
+
−
<th></th>
+
−
<th>0.436
+
−
</th>
+
−
</tr>
+
−
<tr>
+
−
<th></th>
+
−
<th>Asymp. Sig. (2-tailed)
+
−
</th>
+
−
<th></th>
+
−
<th>0.991
+
−
</th>
+
−
</tr>
+
−
</tbody>
+
−
</table>
+
−
</div>
+
−
<div class="mainbody">
+
−
The peak areas of the liquid chromatography solutions of the experimental group (1) (CIP solution of CrpP addition after 30 minutes) and the control group (2) (CIP solution of no CrpP after 30 minutes) are shown in the following table:
+
−
</div>
+
−
<div class="mainbody">
+
−
<div class="table-responsive" >
+
−
<table class="table table-bordered table-hover" >
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−
<caption>Table 2 Peak area of experimental group and control group after 30 minutes</caption>
+
−
<tbody>
+
−
<tr>
+
−
<th>Test number</th>
+
−
<th>Group</th>
+
−
<th>Peak area of liquid chromatography solution</th>
+
−
</tr>
+
−
<tr>
+
−
<th>1</th>
+
−
<th>1</th>
+
−
<th>408173</th>
+
−
</tr>
+
−
<tr>
+
−
<th>2</th>
+
−
<th>1</th>
+
−
<th>405072</th>
+
−
</tr>
+
−
<tr>
+
−
<th>3</th>
+
−
<th>1</th>
+
−
<th>406560</th>
+
−
</tr>
+
−
<tr>
+
−
<th>4</th>
+
−
<th>1</th>
+
−
<th>406027</th>
+
−
</tr>
+
−
<tr>
+
−
<th>5</th>
+
−
<th>1</th>
+
−
<th>401541</th>
+
−
</tr>
+
−
<tr>
+
−
<th>6</th>
+
−
<th>1</th>
+
−
<th>401222</th>
+
−
</tr>
+
−
<tr>
+
−
<th>7</th>
+
−
<th>1</th>
+
−
<th>401478</th>
+
−
</tr>
+
−
<tr>
+
−
<th>8</th>
+
−
<th>1</th>
+
−
<th>402695</th>
+
−
</tr>
+
−
<tr>
+
−
<th>9</th>
+
−
<th>1</th>
+
−
<th>405444</th>
+
−
</tr>
+
−
<tr>
+
−
<th>10</th>
+
−
<th>1</th>
+
−
<th>404834</th>
+
−
</tr>
+
−
<tr>
+
−
<th>11</th>
+
−
<th>1</th>
+
−
<th>401366</th>
+
−
</tr>
+
−
<tr>
+
−
<th>12</th>
+
−
<th>1</th>
+
−
<th>398795</th>
+
−
</tr>
+
−
<tr>
+
−
<th>13</th>
+
−
<th>1</th>
+
−
<th>395506</th>
+
−
</tr>
+
−
<tr>
+
−
<th>14</th>
+
−
<th>1</th>
+
−
<th>399605</th>
+
−
</tr>
+
−
<tr>
+
−
<th>15</th>
+
−
<th>1</th>
+
−
<th>407798</th>
+
−
</tr>
+
−
<tr>
+
−
<th>16</th>
+
−
<th>1</th>
+
−
<th>407647</th>
+
−
</tr>
+
−
<tr>
+
−
<th>17</th>
+
−
<th>1</th>
+
−
<th>401679</th>
+
−
</tr>
+
−
<tr>
+
−
<th>18</th>
+
−
<th>1</th>
+
−
<th>402321</th>
+
−
</tr>
+
−
<tr>
+
−
<th>19</th>
+
−
<th>1</th>
+
−
<th>399728</th>
+
−
</tr>
+
−
<tr>
+
−
<th>20</th>
+
−
<th>1</th>
+
−
<th>403798</th>
+
−
</tr>
+
−
<tr>
+
−
<th>21</th>
+
−
<th>1</th>
+
−
<th>400934</th>
+
−
</tr>
+
−
<tr>
+
−
<th>22</th>
+
−
<th>1</th>
+
−
<th>396259</th>
+
−
</tr>
+
−
<tr>
+
−
<th>23</th>
+
−
<th>1</th>
+
−
<th>400199</th>
+
−
</tr>
+
−
<tr>
+
−
<th>24</th>
+
−
<th>1</th>
+
−
<th>403449</th>
+
−
</tr>
+
−
<tr>
+
−
<th>25</th>
+
−
<th>1</th>
+
−
<th>397587</th>
+
−
</tr>
+
−
<tr>
+
−
<th>26</th>
+
−
<th>1</th>
+
−
<th>397587</th>
+
−
</tr>
+
−
<tr>
+
−
<th>27</th>
+
−
<th>1</th>
+
−
<th>401769</th>
+
−
</tr>
+
−
<tr>
+
−
<th>28</th>
+
−
<th>1</th>
+
−
<th>399936</th>
+
−
</tr>
+
−
<tr>
+
−
<th>29</th>
+
−
<th>1</th>
+
−
<th>401857</th>
+
−
</tr>
+
−
<tr>
+
−
<th>30</th>
+
−
<th>1</th>
+
−
<th>401740</th>
+
−
</tr>
+
−
<tr>
+
−
<th>31</th>
+
−
<th>2</th>
+
−
<th>409694</th>
+
−
</tr>
+
−
<tr>
+
−
<th>32</th>
+
−
<th>2</th>
+
−
<th>411826</th>
+
−
</tr>
+
−
<tr>
+
−
<th>33</th>
+
−
<th>2</th>
+
−
<th>401026</th>
+
−
</tr>
+
−
<tr>
+
−
<th>34</th>
+
−
<th>2</th>
+
−
<th>401052</th>
+
−
</tr>
+
−
<tr>
+
−
<th>35</th>
+
−
<th>2</th>
+
−
<th>405574</th>
+
−
</tr>
+
−
<tr>
+
−
<th>36</th>
+
−
<th>2</th>
+
−
<th>404228</th>
+
−
</tr>
+
−
</tbody>
+
−
</table>
+
−
</div>
+
−
</div>
+
−
<div class="mainbody">
+
−
After proving the two groups of data in accordance with the normal distribution, we can use the t test to analyze.
+
−
</div>
+
−
<div class="mainbody">
+
−
Homogeneity of variance test<br>
+
−
σ<sub>1</sub><sup>2</sup> and σ<sub>2</sub><sup>2</sup> is the population variance of the peak areas of the experimental group and the control group respectively.<br>
+
−
s<sub>1</sub><sup>2</sup> and s<sub>2</sub><sup>2</sup> is the sample variance of the peak areas of the experimental group and the control group respectively.
+
−
</div>
+
−
<div class="mainbody" style="text-align: center">
+
−
Null hypothesis H<sub>0</sub>：σ<sub>1</sub><sup>2</sup>=σ<sub>2</sub><sup>2</sup><br>
+
−
Alternative hypothesis H<sub>A</sub>：σ<sub>1</sub><sup>2</sup>≠σ<sub>2</sub><sup>2</sup><br>
+
−
</div>
+
−
<div class="mainbody">
+
−
The value of F is calculated by:
+
−
</div>
+
−
<h2>Student's t test</h2>
+
−
<div class="mainbody">
+
−
The population mean of the peak areas of the experimental group and the control group is μ<sub>1</sub> and μ<sub>2</sub> respectively.<br>
+
−
The sample mean of the peak areas of the experimental group and the control group is x<sub>1</sub> and x<sub>2</sub> respectively.
+
−
 
+
−
</div>
+
−
 
+
−
+
−
</div>
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−
 
+
−
 
+
−
 
+
 
   
 
   
 
  <div class="part">
 
  <div class="part">
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<p>Factor screening</p>
 
<p>Factor screening</p>
 
</div>  
 
</div>  
−
+
 
<div class="mainbody">
 
<div class="mainbody">
 
In the process of degrading ciprofloxacin, we found several factors affecting the degradation rate of CrpP enzyme (y) such as PH (x<sub>1</sub>), temperature (x<sub>2</sub>), ATP concentration (x<sub>3</sub>), Mg<sup>2+</sup> concentration (x<sub>4</sub>), CIP concentration (x<sub>5</sub>)[1]. We chose the Plackett-Burman design to screen the main factors that have significant effects on the degradation rate of the enzyme, and then we will use the important factors to find the optimal combination of degradation rate.
 
In the process of degrading ciprofloxacin, we found several factors affecting the degradation rate of CrpP enzyme (y) such as PH (x<sub>1</sub>), temperature (x<sub>2</sub>), ATP concentration (x<sub>3</sub>), Mg<sup>2+</sup> concentration (x<sub>4</sub>), CIP concentration (x<sub>5</sub>)[1]. We chose the Plackett-Burman design to screen the main factors that have significant effects on the degradation rate of the enzyme, and then we will use the important factors to find the optimal combination of degradation rate.
 
</div>
 
</div>
 
<div class="mainbody">
 
<div class="mainbody">
−
Based on the range of variables provided by the paper and our experimental conditions, we have determined the range of the five independent variables. The variation range and normalized value of x<sub>1</sub>、x<sub>2</sub>、x<sub>3</sub>、x<sub>4</sub>、x<sub>5</sub> are as follows:
+
Based on the range of variables provided by the related paper and our experimental conditions, we have determined the range of the five independent variables. The variation range and normalized value of x<sub>1</sub>、x<sub>2</sub>、x<sub>3</sub>、x<sub>4</sub>、x<sub>5</sub> are as follows:
 
</div>
 
</div>
 
<div class="mainbody">
 
<div class="mainbody">
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</div>
 
</div>
 
<div class="mainbody">
 
<div class="mainbody">
−
The Plackett-Burman design with N=12 is shown in Table 2 and the experimental data are not shown in Table 2. Due to the tight experimental time, we do not have experimental data now. But we will continue to improve this model later.
+
The Plackett-Burman design with N=12 is shown in Table 2 and the experimental data are not shown in Table 2. Due to the limited and urgent time, we do not have enough experimental data at present. But we will continue to improve this model later.
 
</div>
 
</div>
 
<div class="mainbody">
 
<div class="mainbody">
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Plackett-Burman design and analysis is to judge the importance of factors by analyzing the experimental data of the design.
 
Plackett-Burman design and analysis is to judge the importance of factors by analyzing the experimental data of the design.
 
</div>
 
</div>
 +
 +
<div class="bigtitle" id="title_4">
 +
<p>Experiment design</p>
 +
</div>
 
 
−
</div>
 
−
<div class="part">
 
−
<div class="bigtitle" id="title_4">
 
−
<p>Experiment design</p>
 
−
</div>
 
 
<div class="mainbody">
 
<div class="mainbody">
−
Since we have not verified the experiment, we can't get the selected factors temporarily. Here we assume that three factors are selected: pH, temperature and ATP concentration, then we perform the following process.
+
Since we have not implemented all the experiments yet, we have not been able to screen all the factors for the time being. Here we assume that three factors are selected: pH, temperature and ATP concentration, then we perform the following process.
 
</div>
 
</div>
 
<div class="mainbody">
 
<div class="mainbody">
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</div>
 
</div>
 
<div class="mainbody">
 
<div class="mainbody">
−
\( y=f(x_{1},x_{2},x_{3})\) is unknown, so we need several experiments to estimate \( y=f(x_{1},x_{2},x_{3})\),using the data from the finite experiment. The test point arrangement is shown in Figure 1.
+
\( y=f(x_{1},x_{2},x_{3})\) is unknown, so we need several experiments to estimate \( y=f(x_{1},x_{2},x_{3})\),using the data from the finite experiment. The test point arrangement is shown in Fig. 1[2].
 
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<div class="words">Fig.1 (a)test points for Box-Behnken design (b)test points projection on z<sub>1</sub>, z<sub>2</sub> plane</div>  
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<div class="words">Fig. 1. (a)test points for Box-Behnken design (b)test points projection on z<sub>1</sub>, z<sub>2</sub> plane</div>  
 
 
 
 
 
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After we get the experimental data, we can analyze the experimental data to get the best external degradation conditions. Undoubtedly, We can reduce the cost of the experiments and find the optimal conditions.
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After we get the experimental data, we can analyze the experimental data to get the best external degradation conditions. Finally, we can find the optimal conditions with low experimental cost.
 
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<p>Optimal solution</p>
 
<p>Optimal solution</p>
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Based on the experimental data, we can obtain the regression equation analysis table and get response surface equation using Design Expert 10. Then We will get the partial derivative of the equation and make the derivative zero. By solving the equations, the optimal degradtion conditions can be obtained. In order to verify the effectiveness of the optimization results, we should conduct experiments again under the optimal conditions. If the results are as we expected, undoubtedly we find the best external conditions within the experimental range.
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Based on the experimental data, we can obtain the regression equation analysis table and get response surface equation using Design Expert 10. Then We will get the partial derivative of the equation and make the derivative zero. By solving the equations, the optimal degradation conditions can be obtained. In order to verify the effectiveness of the optimization results, we should conduct experiments again under the optimal conditions. If the results are consistent with our expectation, we find the best external conditions within the experimental range.
 
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                 [1] Chávez-Jacobo, V. M., Hernández-Ramírez, K. C., Romo-Rodríguez, P., Pérez-Gallardo, R. V., Campos-García, J., Gutiérrez-Corona, J. F., ... & Ramírez-Díaz, M. I. (2018). CrpP is a novel ciprofloxacin-modifying enzyme encoded by the Pseudomonas aeruginosa pUM505 plasmid. <p style="display:inline;font-style:italic">Antimicrobial agents and chemotherapy, 62</p>(6), e02629-17.<br>[2] Xu X. H. & He M. Z. (2010). Test design, Design-Expert and SPSS application. Beijing: Science Press.  
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                 [1] Chávez-Jacobo, V. M., Hernández-Ramírez, K. C., et.al. (2018). CrpP is a novel ciprofloxacin-modifying enzyme encoded by the Pseudomonas aeruginosa pUM505 plasmid. <p style="display:inline;font-style:italic">Antimicrobial agents and chemotherapy, 62</p>(6), e02629-17.<br>[2] Xu X. H. & He M. Z. (2010). Test design, Design-Expert and SPSS application. <i>Beijing: Science Press</i>.  
  
 
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Latest revision as of 12:54, 21 October 2019

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Overview

In order to find the optimal degradation conditions for engineered E.coli, we found the main factors affecting the degradation rate from the related paper[1]. Firstly, we used the Plackett-Burman design to screen factors. In the future we can get the important factors by experimental data. Secondly, the Box-Behnken design was used in the experimental design to reflect objective reality with fewer experiments. According to the experimental results, the response surface equation can be obtained, and optimal degradation conditions can be found. Finally, after obtaining the extreme value of the equation (optimal degradation conditions), it can be verified by experiments in the future.

Goals

1. Screen all factors to obtain important factors affecting the degradation rate of CrpP enzyme
2. Find the optimal working conditions for engineered E.coli
3. To achieve the optimal CIP degradation rate with as little experimental cost as possible.

Factor screening

In the process of degrading ciprofloxacin, we found several factors affecting the degradation rate of CrpP enzyme (y) such as PH (x1), temperature (x2), ATP concentration (x3), Mg2+ concentration (x4), CIP concentration (x5)[1]. We chose the Plackett-Burman design to screen the main factors that have significant effects on the degradation rate of the enzyme, and then we will use the important factors to find the optimal combination of degradation rate.
Based on the range of variables provided by the related paper and our experimental conditions, we have determined the range of the five independent variables. The variation range and normalized value of x1、x2、x3、x4、x5 are as follows:
Table 1 Levels of the variables of Plackett-Burman design
Name Variable Low level(-1) Zero level(0) High level(1)
x1 Initial pH 6 7 8
x2 Temperature(℃) 31 34 37
x3 ATP concentration(mmol/L) 1.7 2 2.3
x4 Mg2+concentration(mmol/L) 8 10 12
x5 CIP concentration(μg/ml) 0.5 1 1.5
The Plackett-Burman design with N=12 is shown in Table 2 and the experimental data are not shown in Table 2. Due to the limited and urgent time, we do not have enough experimental data at present. But we will continue to improve this model later.
Table 2 The Plackett-Burman experimental design with five independent variables
Test number x1 x2 x3 x4 x5
1 -1 1 -1 1 1
2 -1 -1 -1 1 -1
3 -1 1 1 -1 1
4 1 -1 1 1 1
5 1 1 -1 -1 -1
6 1 1 1 -1 -1
7 1 -1 -1 -1 1
8 -1 1 1 1 -1
9 -1 -1 1 -1 1
10 1 1 -1 1 1
11 -1 -1 -1 -1 -1
12 1 -1 1 1 -1
We can analyze five variables by ANOVA and observe their p-values to determine their degree of effect on the experimental index y. If the p value of a variable is greater than 0.05, the effect of this variable on y is not significant. Based on this way, we can screen out the important factors, and then carry out the Box-Behnken design on the selected factors to find the optimal external factors.
Plackett-Burman design and analysis is to judge the importance of factors by analyzing the experimental data of the design.

Experiment design

Since we have not implemented all the experiments yet, we have not been able to screen all the factors for the time being. Here we assume that three factors are selected: pH, temperature and ATP concentration, then we perform the following process.
In order to find the optimal external conditions in the degradation process and reduce the number of experiments to save costs, we used Box-Behnken design to arrange experiments.
Firstly, we need to find quantitative relationship between Ciprofloxacin degradation rate(y) and initial pH (x1), temperature (x2) and ATP concentration (x3). Quantitative relationships can be expressed as: \[ y=f(x_{1},x_{2},x_{3}) \]
\( y=f(x_{1},x_{2},x_{3})\) is unknown, so we need several experiments to estimate \( y=f(x_{1},x_{2},x_{3})\),using the data from the finite experiment. The test point arrangement is shown in Fig. 1[2].
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Fig. 1. (a)test points for Box-Behnken design (b)test points projection on z1, z2 plane
The maximum and minimum values of x1, x2, x3 are called upper levels and lower levels and the average of upper levels and lower levels is zero levels. Taking into account the limitations of actual factors, the variation range is as follows.
Table 3 Levels of the variables of Box–Behnken design
Name Variable Low level(-1) Zero level(0) High level(1)
x1 Initial pH 6 7 8
x2 Temperature(℃) 31 34 37
x3 ATP concentration(mmol/L) 1.7 2 2.3
The test points of the Box-Behnken design is shown in the following table:
Table 4 The Box–Behnken experimental design with three independent variables
Test number x1 x2 x3
1 0 1 -1
2 -1 1 0
3 0 -1 1
4 -1 0 1
5 1 1 0
6 1 0 1
7 1 -1 0
8 0 0 0
9 0 1 1
10 1 0 -1
11 -1 0 -1
12 0 0 0
13 -1 -1 0
14 0 0 0
15 0 0 0
16 0 0 0
17 0 -1 -1
After we get the experimental data, we can analyze the experimental data to get the best external degradation conditions. Finally, we can find the optimal conditions with low experimental cost.

Optimal solution

Based on the experimental data, we can obtain the regression equation analysis table and get response surface equation using Design Expert 10. Then We will get the partial derivative of the equation and make the derivative zero. By solving the equations, the optimal degradation conditions can be obtained. In order to verify the effectiveness of the optimization results, we should conduct experiments again under the optimal conditions. If the results are consistent with our expectation, we find the best external conditions within the experimental range.

References

[1] Chávez-Jacobo, V. M., Hernández-Ramírez, K. C., et.al. (2018). CrpP is a novel ciprofloxacin-modifying enzyme encoded by the Pseudomonas aeruginosa pUM505 plasmid.

Antimicrobial agents and chemotherapy, 62

(6), e02629-17.
[2] Xu X. H. & He M. Z. (2010). Test design, Design-Expert and SPSS application. Beijing: Science Press.
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